Generalized mildly nonconvex variational inequalities and its solvability

Balwant Singh Thakur, Suja Varghese
2012 Journal of Nonlinear Analysis and Application  
Using the prox-regularity notion, we introduce and study a generalized mildly nonconvex variational inequality. We study existence and iterative approximation of its solution under the partially relaxed cocoercivity. Several consequences of the proposed nonconvex variational inequality are also discussed. Journal of Nonlinear Analysis and Application 2 alternative formulation of variational inequalities as multivalued inclusions. Bounkhel et al. [1], Noor [8], Pang et al. [11] has considered
more » ... ] has considered variational inequalities in the context of uniformly prox-regular sets. It is known that the uniformly prox-regular sets are nonconvex and include the convex sets as special cases (see [2] ). Recently Noor [9] studied strongly nonlinear nonconvex variational inequalities involving two single valued nonlinear operators. Motivated by the works going in this direction, we will study a nonconvex variational inequality involving two set-valued nonlinear mappings. We establish the existence of the solution of this problem. We also study iterative approximation of its solution.
doi:10.5899/2012/jnaa-00146 fatcat:jxv3fmigobal7nmbu4e5pax25u